This homework is about the properties of the nearest stars to the Sun and the brightest stars in the sky. Some of these properties are summarised in tables in Appendix 5 of the textbook (pages A-13 to A-16). "Visual brightness" refers to how bright the star looks on the sky, relative to the Sun, and "visual luminosity" refers to the actual power output of the star (energy per unit time), in units of solar luminosity. Answer the following questions. In all cases, the questions refer to stars other than the Sun.

1. Which is the most luminous star on the lists? (Call this Star 1).____________
   
2. Is this the hottest star on the lists?____________
   
3. What property of the stars do you base this on?_______________
   
4. How many stars on the lists are hotter than Star 1?___________
   
5. Since hot stars are more luminous than cool stars, why is Star 1 the most luminous star on the lists?
   
   
   
   
   
   
6. Of all the stars hotter than Star 1, which is the least luminous? (Call this Star 2)________________
   
7. What is significant about Star 2?
   
   
   
   
   
   
8. How do you reconcile your answers to the previous two questions?
   
   
   
   
   
   
9. Imagine a big sphere centered on the Sun and containing Star 1, the most luminous star. Compare the volume of this sphere with the volume of the sphere containing all the nearby stars, i.e., the stars on the first list (i.e., calculate the ratio of the volumes.)
   
   
   
   
   
   
   
   
   
   
   
10. Are there any nearby stars with the same luminosity class as Star 1?____________
    
11. How many main sequence stars are there in the local sample?____________
    
12. What do your answers to the previous two questions tell you about the relative scarcity of main sequence and supergiant stars?
    
    
    
    
    
    
13. Find another star that has the same temperature as Star 1:_______________
    
14. Recall the relation among a star's luminosity, temperature and radius. Calculate the relative sizes of Star 1 and this star (i.e., the ratio of their radii).
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
15. Describe briefly the processes going on near the core of Star 1.